How can I get the requests of my Google AppEngine application to perform better and faster (i.e. less load times and less CPU usage)? I'm specifically referring to imporvements for the server-side portion of the app, and not the client-side.

This is not really an optimization but the choice of framework is really important here. Most legacy framework in Java and Python(Django,..) are not designed to startup fast because it just isn't important in traditional hosting. Consider using an App Engine specific framework like Tipfy, Kai, Webapp, ... (Python) or slim3, ... (Java).

Ideally, you should organize your data so that each user request needs only one call to the datastore, preferably a db.get because queries are significantly slower. To achieve this, you'll often need to denormalize your data, and maintain the different copies in sync using entity groups and transactions.

When making more than one urlfetch or API call, you can speed up the process by making the calls in parallel using the non-blocking(async) syntax. Caching whenever possible is of course really important too.

If you haven't yet, I recommend watching Google's IO talks (2010 & 2011), in particular this year's Scaling App Engine Applications which does a very good job of describing server-side best practices.

I use memcache which significantly increased my app's performance. I hope it also can be usable for you. When using memcache in combination with a HTTP header setting the cache-control I've gotten significant improvements in response times.